A Priority Move referes to a move/action that allows a player's Pokemon to move first, regardless of its speed compared to the opponent's speed.
The higher the Priority Rating, the more 'priority' it is granted.
There are seven levels of priority moves, and it really depends on both players actions:
If one player switches Pokemon, that would be a 6th Level Priority move. (It is topped by only one move: the only 7th Level Priority move: Pursuit)
The only 5th Level Priority move is Helping Hand. It goes before most other Priority moves.
There are two 4th Level Priority moves: Magic Coat and Snatch.
There five 3rd Level Priority moves: Detect, Endure, Fake Out, Follow Me, and Protect. I believe that it depends on Speed here if these specific moves are used against each other on the same turn.
The only 2nd Level Priority move is Feint, designed to be Priority, and at the same time, be one level below Protect. Nice.
Here's the long section: All the 1st Level Priority moves are as follow, and depend on Speed if they are uses against each other at the same time: Aqua Jet, Bide, Bullet Punch, Extremespeed, Ice Shard, Mach Punch, Quick Attack, Shadow Sneak, Sucker Punch, and Vacuum Wave.
The 0th Level Priority moves don't exist. They are the normal moves otherwise.
Note: Levels 1-6 are ordered as they would go in battle. Pursuit, the only seventh level, is normally a 0th Level, but goes before everything ONLY IF uses on the same Pokemon on the same turn that tries to switch out.
Technically, Level 1-7 are the only Priority moves, except for Pursuit, which is circumstantial. However, these moves are Reverse Priorities. They go after normal moves.
The rating system is the reversed. -1st Levels go directly after normal moves. NOTHING goes after a -7.
The only -1st Level Priority move: Vital Throw. Simple.
For whatever reason, there are no -2nd moves. If this doesn't make sense to some people, I'm with you. I'm sure whoever planned that had a reason.
The only -3rd Level Priority move is Focus Punch.
There are two -4th Level Priority moves: Avalanche and Revenge.
There's only one -5th Level Priority move: Counter I thought Mirror Coat would go in this group as well, but apparently, it's a Priority move. Huh.
The two -6th Level Priority moves are Roar and Whirlwind. I don't know why they are Reverse Priorities, but just go with it.
The only -7th Level Priority move is... (drumroll)... Trick Room.